Question

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x=10 u-7 v+5 w, y=2 u+7 v-2 w, and z=7 u+4 v-7 w implies ∂(x, y, z)/∂(u, v, w)=

Answer 1

To find the partial derivative of (x, y, z) with respect to (u, v, w), we need to differentiate each component separately. The partial derivatives are (10, -7, 5), (2, 7, -2), and (7, 4, -7) respectively.

Step-by-step explanation:

The question is asking for the partial derivative of (x, y, z) with respect to (u, v, w). To find this derivative, we need to differentiate each component of (x, y, z) with respect to (u, v, w) separately.

For x, the derivative with respect to u is 10, with respect to v is -7, and with respect to w is 5.

Similarly, for y, the derivative with respect to u is 2, with respect to v is 7, and with respect to w is -2.

And for z, the derivative with respect to u is 7, with respect to v is 4, and with respect to w is -7.

Therefore, the partial derivative of (x, y, z) with respect to (u, v, w) is (10, -7, 5), (2, 7, -2), (7, 4, -7).